# Born-Haber Cycle - Formation

## Key Questions

• It is not specific to any chemical.

The Born-Haber cycle is a way of calculating energies such as the enthalpy of lattice dissociation, by breaking this down into a series of individual steps and working out the energy change associated with each small step - basically a Born-Haber cycle is a way of using Hess's Law.

For example, the enthalpy of lattice dissociation refers to taking a giant ionic lattice in the solid state, and splitting it up into individual ions, all sufficiently far apart that they don't influence each other. If we can't measure this directly, we could calculate it by considering the energy change when the lattice was formed from its elements (enthalpy change of formation), the energy changes needed to atomise those elements, and the energy changes needed to turn each atom into the relevant ion. Combining those energy changes would give the enthalpy of lattice dissociation.

• The Born - Haber Cycle is usually used to calculate lattice enthalpies.

For sodium chloride this is $\Delta H$ for:

$N {a}_{\left(g\right)}^{+} + C {l}_{\left(g\right)}^{-} \rightarrow N a C {l}_{\left(s\right)}$

This can also be calculated using a theoretical electrostatic model assuming that the substance is made from discrete ions.

The work done in separating 2 charges ${q}_{1}$ and ${q}_{2}$ from a distance $r$ to infinity is given by:

$W \propto - \frac{{q}_{1} {q}_{2}}{r}$

Where $r$ is the separation.

By extending this idea to 3 dimensions we can calculate a "theoretical" value for the lattice enthalpy. By comparing the value of the experimental Born - Haber values with those obtained from the theoretical model we can get a measure of the ionic character of the bond.

Sodium chloride gives a very good agreement indicating that the ionic model we use is a good one. There is much more discrepancy between the values for silver chloride indicating more covalent character than would be expected if it were $A {g}^{+} C {l}^{-}$.

• Hello, I make a series of youtube tutorial videos explaining chemistry concepts for high schoolers.

The Born-Haber cycle is designed to measure lattice energy. Ionic compounds form crystal structures called lattices. To melt or dissolve the ionic compound, you must break that lattice. The energy required to do this is called "lattice energy."

The Born-Haber cycle itself is a shortcut method. We use something called Hess's law to avoid a lot of messy calculations. Hess's law states that the energy it takes to make a compound is equal to the the energies of the products minus the energies of the reactants. So Born-Haber uses the concept to state that the lattice energy is equal to the energy required to make each element a gas and then ionize it.

To shorten that explanation: The Born-Haber cycle allows you to figure out how easy or hard an ionic compound is to melt using a standard heat of formation table.

Hope this helps!